Assignment 3 Team Project Outline(Complete by Sunday, Nov. .docx

Assignment 3: Team Project Outline
(Complete by Sunday, Nov. 20)
Due No Due Date Points 50 Submitting a file upload
Start Assignment
This assignment is due in this Module.
This assignment aligns with Learning Outcomes 1, 2 and 4.
Directions
For this project you will work in a collaborative team to
identify a political issue. Your
team will then research, analyze, develop, and defend a position
within that issue. The
end product will be a paper that describes the issue and supports
your team’s
position. Remember, your goal is to select an issue, take a
position, and develop a
paper to support that position.
Political issues could include discussions on healthcare,
immigration reform,
American’s marijuana debate, tax reform, religious freedom act,
LGBTQ rights, and,

etc. If you are unsure of what constitutes a valid political issue,
please check with the
instructor for guidance in this area.
The outline should minimally contain the following sections:
1. Brief introduction and thesis statement
2. Overview of the issue (research including at least 5
references)
3. The team's position
11/15/22, 11:25 PM
Page 1 of 4
Team Project Outline Rubric
Criteria Ratings Pts
25 pts
4. Rationale for your position (research including at least 5
references)
5. Summary, conclusions and recommendations
Submission
A designated member will be the one who submits this
assignment. This assignment

requires a file upload submission. After you have reviewed the
assignment instructions
and rubric, as applicable, complete your submission by
selecting the Submit
Assignment button next to the assignment title. Browse for your
file and remember to
select the Submit Assignment button below the file to complete
your submission.
Review the confirmation annotation that presents after
submission.
Grading
This assignment is worth 50 points toward your final grade and
will be graded using
the Project Outline Rubric. Please use it as a guide toward
successful completion of
this assignment.
(1)
Organization 25 to >22.0 pts
Exemplary
The outline is
logically
organized with a

well-written
introduction,
thesis statement
and conclusion.
22 to >19.0 pts
Meets
Expectations
The outline is
logically
organized with a
well-written
introduction,
thesis statement
19 to >13.0 pts
Developing
The outline is
logically
organized with a

well-written
introduction,
thesis statement
and conclusion.
13 to >0 pts
Beginning
The outline is
loosely
organized with
an
introduction,
thesis
statement, and
11/15/22, 11:25 PM
Page 2 of 4
15 pts
10 pts

and conclusion.
One of these
requires
improvement.
One or more of
the introduction,
thesis statement,
and/or
conclusion
require
improvement.
conclusion.
The
introduction,
thesis
statement,
and/or
conclusion

require much
improvement.
Topic
Overview
15 to >13.0 pts
Exemplary
Provides an
overview that
comprehensively
describes the
selected
political issue.
The description
is clearly
supported with
the number of
scholarly
sources noted.
13 to >11.0 pts

Meets
Expectations
Provides an
overview that
comprehensively
describes the
selected
political issue.
The description
is clearly
supported with
fewer than the
number of
scholarly
sources noted
and is slightly
underdeveloped.
11 to >8.0 pts

Developing
Provides an
overview that
comprehensively
describes the
selected
political issue.
The description
is somewhat
supported with
at least one
scholarly source
and is
underdeveloped.
8 to >0 pts
Beginning
Few sources
cited can be

considered
appropriate and
from accepted
sources.
Attempts to
provides an
overview of the
selected
political issue.
However, the
description is
not supported
with scholarly
sources and is
significantly
underdeveloped.
Quality of
Work
10 to >8.0 pts

Exemplary
Quality of
writing is
exceptional
with no
spelling,
grammar, or
mechanical
8 to >7.0 pts
Meets
Expectations
Quality of
writing is good
with minor
spelling,
grammar, or
mechanical
7 to >5.0 pts

Developing
Quality of writing
is acceptable
with minor
spelling,
grammar, or
mechanical
errors that
5 to >0 pts
Beginning
Quality of writing
is unacceptable
with many
spelling,
grammar, or
mechanical
errors that
11/15/22, 11:25 PM

of 4
Total Points: 50
errors. Writing
is organized
and well
developed.
errors that do
not interfere
with
comprehension.
usually do not
interfere with
comprehension.
significantly
interfere with
comprehension.
11/15/22, 11:25 PM
Page 4 of 4

library(MASS)
data("Boston")
colnames(Boston)
model_full <- lm(medv~., data = Boston)
summary(model_full)
model_1 <- lm(medv~crim+zn, data = Boston)
# Manually select
summary(model_full)
summary(model_1)
AIC(model_full); BIC(model_full)
AIC(model_1); BIC(model_1)

# Best Subset
install.packages('leaps')
library(leaps)
# regsubsets only takes data frame as input
subset_result <-
regsubsets(medv~.,
data=Boston,
nbest=2,
nvmax = 14)
summary(subset_result)
plot(subset_result)
# Backward Elimination
nullmodel <- lm(medv~1, data=Boston)
summary(model_full)
# has fitted: model_full <- lm(medv~., data=Boston)
model_step_b <- step(model_full, direction='backward')

# Forward Selection
model_step_f <- step(nullmodel,
scope=list(lower=nullmodel, upper=model_full),
direction='forward')
# Stepwise Selection
model_step_s <- step(nullmodel,
scope = list(lower=nullmodel, upper=model_full),
direction='both')
Instruction of Lab 8
EBTM 350, Fall 2022, Professor: Xiaorui Zhu, Ph.D.
Purpose: I hope that by doing this lab, you will get a taste of
how to prepare your final project, as well
as (1) practice your R coding; (2) get an idea of the entire
process (Exploratory Data Analysis,
regression modeling, data mining, interpreting results, etc.); and

(3) realize that data
understanding and result interpretation are not trivial tasks, and
they are extremely important in
business projects. Submit a Word file with all the following
sections and results well organized.
Requirements:
1. (5 points) Write an interesting story in the first section
(Background or Introduction). In my class case, we
want to forecast the median home value in the Boston area (or
the wine-tasting preference), but I would
refrain from offering you a specific context. I require you to
think about in what situations, you may need to
forecast the median home price for your business/clients and
write down your story.
a. For example, you can pretend you are a real estate buyer
agent. Your decision is to give a
recommendation for your client (buyer) to make a reasonable
offer for the house they are interested in.
So, you want to predict the median house price in a certain area
with attributes so that your clients can
use it as a reference to make the offer.
b. Another simple example: From an analyst’s perspective, I
want to understand how these predictors are
associated with the median home price. What are those major

contributors? So, when I want to buy a
house, I should focus on these important attributes because they
highly affect the market value of the
house.
c. Yours.
2. (10 points) Exploratory Analyses & Visualization.
a. (2 pts) Explore the data (use plots, summary statistics, etc.)
and provide some findings and your
interpretation.
b. (2 pts) Explore the response variable: median house value
(use visualization tools, check outliers, etc.).
c. (2 pts) Explore some of the predictors that you believe are
important (use visualization tools, check
outliers, etc.).
d. (4 pts) Explore the associations between predictors and your
response variable visually and
quantitatively.
3. (20 points) Modeling and Interpretation of your results.
a. (6 pts) Use multiple linear regression models we just learned.
You may need to explore models with
different predictors and find the best one.

b. (6 pts) Use at least one variable selection method we learned
this week (Best subset selection, Forward,
backward, stepwise selection) to find the best model.
c. (8 pts) Interpret the fitted model from multiple perspectives:
find these significant predictors by t-test (2
pts), interpret the coefficient estimates (4 pts), and check
whether the whole model is significant (F-
test) (2 pts).
4. (5 points) Summary or Conclusion:
a. (2 pts) Compare all the models you obtained (Use information
criteria AIC/BIC, and goodness-of-fit R2 to
support your conclusion).
b. (2 pts) Provide a suggestion of the best model.
c. (1 pts) Conclude your findings: what predictors are useful,
what is the performance of your model etc.
To: Mr. Zhu, Director of Investment Analysis
From: Lexi Cioffi, Investment Analysis Intern
Date: November 11, 2022
Subject: Boston Housing Exploratory Analysis
Introduction
As an intern at the Investment Analysis Group, I have prepared

this evaluative report in order to make
recommendations for investors on which residential properties
are the best to invest in within the Boston
area. Recently, our new clients asked our firm to determine the
variables that most significantly influence
the median home value in Boston in order to make a
recommendation of which residential properties
within the area are the best to invest in. It is important for our
clients to know what variables significantly
influence median home value in order to make wiser
investments and hopefully increase their return on
investment. There are 14 values that I will use throughout my
analysis: CRIM (per capita crime rate by
town), ZN (proportion of residential land zoned for lots over
25,000 sq. ft.), INDUS (proportion of non-
retail business acres per town), CHAS (Charles River dummy
variable; 1 if tract bounds river; 0
otherwise), NOX (nitric oxides concentration; parts per 10
million), RM (average number of rooms per
dwelling), AGE (proportion of owner-occupied units built prior
to 1940), DIS (weighted distances to five
Boston employment centers), RAD (index of accessibility to
radial highways), TAX (full-value property-
tax rate per $10,000), PTRATIO (pupil-teacher ratio by town),
B (1000(Bk-0.63)^2 where Bk is the
proportion of blacks by town), LSTAT (% lower status of the
population), and MEDV (median value of
owner-occupied homes in $1000’s). Our clients would like us to
consider all of the variables in our
evaluation, and then present to them the most significant as well
as the least significant variables that play
a role in predicting the median home value within the Boston
area.
Exploratory Analyses and Visualization

Before conducting a full linear regression analysis, I began by
exploring the Boston Housing Data using
plots and summary statistics. Using the R code
summary(Boston) I was able to retrieve summary statistics
on each of the 14 variables. For a more specific description of
the quantities that I retrieved, please
reference Figure 1.
Figure 1. Summary statistics of the
Boston Housing Data, providing
values of minimum, maximum,
mean, median, and interquartile
range for each of the 14 variables.
After evaluating the summary data for each of the 14 variables,
I noticed that there was a significant range
of values for the majority of the variables being examined. This
extent of variation confirms that a model
is absolutely necessary in order to best capture all of the data as
well as to predict which variables have an
influence on the median home value.

Evaluating Predictor Variables
I then decided to investigate individual variables that I felt
would hold a greater influence on the median
home value in Boston, as well as those that I felt are the most
relevant when evaluating a residential
property investment. The three variables that I chose to
investigate were: crim, age, and tax.
Figure 2. Histogram of the per capita crime rate by town
in the Boston area.
Figure 3. Histogram of the proportion of owner-occupied
units built prior to 1940.

Figure 4. Histogram of the full-value property-tax per
$10,000.
I created a histogram for each of the three determined variables
using the following R code:
hist(Boston$crim, c = “blue”), hist(Boston$age, c = “blue”),
hist(Boston$tax, c = “blue”). From the
three figures above, I was able to draw conclusions about the
range of the variables as well as the relative
frequencies of their values. Figure 1 demonstrates that the per
capita crime rate per town most commonly
falls between the range of 10 and 20, with very few responses
having a value above 20. Figure 2
demonstrates that the proportion of owner-occupied units built
prior to 1940 ranges from a proportion of
0 to a proportion of 100, with the most common segment being
a proportion between 90 and 100. Finally,
Figure 3 demonstrates that the full-value property-tax per
$10,000 does not have any data that falls
between the range of 500 and 650, and that the most frequent
value fall between the range of 650 and 700.
Evaluating the Response Variable
When looking at the response variable, medv, I used a boxplot

in order to spot potential outliers and gain
a visual representation of the data using R code
boxplot(Boston$medv). I also made a histogram with the
median home value data in order to get a different visual
representation of the data using R code
hist(Boston$medv, c = “blue”).
Figure 5. Boxplot of the median value of
owner-occupied homes in the Boston area.
Figure 6. Histogram of the median value of
owner-occupied homes in the Boston area.
Figures 5 above shows the extensive number of outliers that
exist in the median value data. The median of
the median value data is around 22, with values approximately

38 or greater being considered outliers in
the data set. Figure 6 confirms these findings. The histogram of
the median value of owner-occupied
homes shows that the most frequent value is between 20-25,
with the second most frequent between 15-
20.
Predictor Variable Associations
After evaluating the three predictor variables that I felt were
most significant (crim, age, tax) and the
response variable (medv) on their own, I evaluated the
correlations that exist between those variables in
order to gain additional insight into the data set. To explore the
associations between these variables and
the median home value, I decided to utilize scatterplots as well
as calculate the correlation coefficient that
exists between the two variables using R code
plot(Boston$medv~Boston$crim, main="Scatterplot of
medv Against crim", xlab = "crim", ylab = "medv", pch=16) and
cor(Boston$medv, Boston$crim).
Figure 7. Scatterplot of median value of owner-
occupied homes and crime rate per capita by town.
Correlation coefficient: -0.388

occupied homes and proportion of owner-occupied
units built prior to 1940.
occupied homes and full-value property-tax rate per
$10,000.
Figure 7 represents the relationship between the median home
value and the per capita crime rate per
town. With a correlation coefficient of -0.388, the variables can
be said to have a negative correlation.
Having a negative correlation signifies that as the median home

value decreases, the crime rate increases,
or that as the median home value increases, the crime rate
decreases. The scatterplot demonstrates the
trend of negative correlation. Figure 8 represents the
relationship between the median home value and the
proportion of owner-occupied homes built prior to 1940. With a
correlation of coefficient of -0.378, the
variables can be said to have a negative correlation. The
scatterplot demonstrates the relationship of
negative correlation because as the age range increases, the
median home value generally decreases.
Figure 9 represents the relationship between the median home
value and the full-value property-tax rate.
With a correlation coefficient of -0.469, the variables can be
said to have a negative correlation that is
even stronger than that of the crim and age variables. The
scatterplot demonstrates this negative
correlation because as the property-tax rate increases, the
median home value generally decreases.
Modeling and Interpretation of Results
In order to evaluate the significance that variables have in
predicting the median home value in Boston, I
began with a model that accounted for all 14 variables that I
was given, using R code model_full <-
lm(medv ~ ., data = Boston). One other model that I wanted to
create was one only accounting for the
three variables I felt were most impactful in investment
selection: crim, age, and tax. I created this second
model, called model1, using R code model_1 <- lm(medv ~ crim
+ age + tax, data = Boston). I received
summary statistic information for both of these models using R
code summary(model_full) and
summary(model1).

Figure 10. Summary statistics of the full variable
model, including all 14 predictor variables within
the Boston Housing Data. Estimate coefficients
and their significance as well as the coefficient of
determination for the model are included.
Figure 11. Summary statistics of the model
accounting for the previously selected crim, age,
and tax variables within the Boston Housing Data.
Estimate coefficients and their significance as well
as the coefficient of determination for the model
are included.
Between these two models, it can be interpreted that the full
model is better than model1. The coefficient
of determination, R2, for the full model is 0.7406, whereas the
R2 value for model1 is 0.2624. When
evaluating models, the model with the highest coefficient of
determination is the better fitted model.

Because the model1 R2 value is so low, it is unlikely that the
three selected predictor variables carry
heavy significance in predicting the median home value,
holding all other variables constant.
Determining the Best Model
With my three selected predictor variables producing the worse
model, I decided to determine the best
model by beginning with all 14 of the predictor variables in the
Boston Housing Data. My initial goal was
to find the best model that accounted for 3 of the predictor
variables, holding all other predictor variables
constant. To determine which 3 size model was the best
determinant of median home value, I used R code
bestsub <- regsubsets(medv ~., data=Boston, nbest=3, nvmax =
14). I then created a plot to visualize the
predictor variables using R code plot(bestsub)
Figure 12. A plot demonstrating the best subsets to
create a size 3 model that best predicts the median
home value in the Boston Housing Data.
Upon examining the figure above, I determined that the best
size 3 model, holding all other variables

constant, accounts for the variables rm, ptratio, and lstat. On the
chart, these variables appear first with the
lowest associated BIC, and the lower the BIC, the better the
model. The R code for this model is
model_best <- lm(medv ~ rm + ptratio + lstat, data = Boston).
Using R code summary(model_best) I
determined that the coefficient of determination for this model
is 0.6786, indicating that there is a better
model, though my model_best was the best model that existed
when accounting for only 3 of the
predictor variables.
In order to find the model that best predicts the Boston Housing
Data, I first established a null model to
which I could compare my best fitted model to using R code
nullmodel <- lm(medv~1, data=Boston). In
order to determine the best model, I decided to proceed with the
backward selection method, using R code
model_step_b <- step(model_full, scope=list(lower=nullmodel,
upper=model_full), direction =
‘backward’).
Figure 13. Data demonstrating the backward
model selection method for the Boston Housing
Data.

After evaluating the backward selection method, I determined
that the best model for predicting the
median value of homes in the Boston area is one that includes
all of the predictor variables except for the
age and indus variables. In the backward selection method, it is
shown that removing age and indus will
provide the lowest AIC value. Because the lower the AIC, the
better the model, those two variables are
the only two which need to be removed in order to further
decrease the AIC. On the other hand, the
backward selection method tells us that the worst variables to
eliminate from the model, in order, are:
lstat, rm, and dis. This finding is relatively consistent with the
model that I made above which included
only the three best predictor variables to use in a model. This
means that the model which best predicts
the median home value can be established using R code:
bestmodel <- lm(medv ~ . - indus - age, data =
Boston)
After running the best model, the coefficients for each of the
included variables were as follows: intercept
36.341, crim -0.108, zn 0.046, chas 2.72, nox -17.378, rm
3.802, dis -1.49, rad 0.300, tax -0.012, ptratio -
0.947, black 0.009, lstat -0.523. An example interpretation of
the coefficient of rm would be that 1
additional room in a home impacts the median home value by a
factor of 3.802, holding all other variables
constant. Within this model, the p values for each of the

coefficients are less than 0.05, indicating that the
findings are statistically significant. This means that I reject the
null hypothesis that there is no
association between the predictor variables and the response
variable. Additionally, the p value of the f-
test is also smaller than 0.05, meaning that at least one of the
predictor variables has an impact on the
response variable and does not have a coefficient of 0.
Conclusion
After concluding my analysis, I have determined that the
following model is the most significant in
determining the median home value in Boston: medv ~ . – indus
– age. I believe that the predictor
variables indus and age should not be included in a model to
determine the median home value in Boston
because they increase the value of the AIC. The model
accounting for all of the response variables has an
AIC value of 1589.6, whereas the model without the indus and
age variables has a lower AIC value of
1587.7. Additionally, in the best model, the R2 value is 0.7406,
meaning that 74.06% of the variation in
the data is explained by the model. Additionally, we can tell our
clients that when considering their future
residential investments in the Boston area, the three most
important variables to consider are rm, ptratio,
and lstat – if they are only wishing to consider the three most
important variables.

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